Question

Rewrite each of the following expressions as a single logarithm. That is, each answer should contain only one log (or ln) expression.

log_2(x) + log_2(y)

a) log_2(xy)
b) log_2(x/y)
c) log_2(x + y)
d) log_2(x - y)

Answer 1

To rewrite each expression as a single logarithm, you can use the properties of logarithms. Some expressions can be simplified using these properties, while others cannot.

Step-by-step explanation:

To rewrite each of the given expressions as a single logarithm, we can apply the properties of logarithms. Let's go through each expression:

a) log2(xy)

Since the expression is already in the form of log2(xy), it is already a single logarithm.

b) log2(x/y)

We can apply the quotient property of logarithms, which states that logb(x/y) = logb(x) - logb(y).

So, log2(x/y) = log2(x) - log2(y).

c) log2(x + y)

We cannot rewrite log2(x + y) as a single logarithm because the addition of x and y inside the log cannot be simplified further.

d) log2(x - y)

We also cannot rewrite log2(x - y) as a single logarithm because the subtraction of x and y inside the log cannot be simplified further.